Find the area of a regular 12-sided polygon with a side of length \( s \) and an apothem of 8.

(Give your answer in terms of \( s \).)

[ If\ this\ is\ regular\ 12-sides\ polygon\ it\ is\ build\ from\ 12\ isosceles\triangles.\\ apothem=height\ of\ triangle\ side=base\ of\ triangle\\ Area\ of\ one\ triangle:\ A=\frac{s apothem}{2}=\frac{s 8}{2}=4s\\ Area\ of\ polygon\ =12 A=12 4s=48s
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Answered by luana | 2024-06-10

apothem is the height of a triangel formed by two consecutive vertices with the center. the are of this triangle = 1/2 s 8 = 4s there area 12 such triangles in the regular 12 side polygon So area = 12 * 4 s = 48 s

Answered by Everest2017 | 2024-06-10

The area of a regular 12-sided polygon with a side length s and an apothem of 8 is calculated as 48 s . This is derived using the area formula for polygons, taking into account the perimeter and the apothem. The final result is 48 s .
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Answered by luana | 2024-10-01